Inspired by shrinking cellular automata (SCA), we investigate another variant of the classical one-dimensional cellular automaton: the shrinking and expanding cellular automaton (SXCA). In addition to the capability to delete some cells as in SCA, an SXCA can also create new cells between already existing ones. It is shown that there are reasonably close (polynomial) relations between the time complexity of SXCA and the space and time complexity of Turing machines and alternating Turing machines respectively. As a consequence the class of problems decidable in polynomial time by SXCA coincides with PSPACE.